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Current Eye Research
2003, Vol. 27, No. 3, pp. 143–149
0271-3683/03/2703-143$16.00
© Swets & Zeitlinger
Revised formulas for summarizing retinal vessel diameters
Michael D. Knudtson1, Kristine E. Lee1, Larry D. Hubbard1, Tien Yin Wong1,2, Ronald Klein1 and Barbara E.K. Klein1
Department of Ophthalmology, University of Wisconsin, Madison, USA; 2Singapore National Eye Center & National
University of Singapore, Singapore
1
Abstract
Background/Purpose. Recent findings suggest that an
objective assessment of retinal vessel caliber from fundus
photographs provide information about the association of
microvascular characteristics with macrovascular disease.
Current methods used to quantify retinal vessel caliber, introduced by Parr1,2 and Hubbard,3 are not independent of scale
and are affected by the number of vessels. To improve upon
these methods we introduce revised formulas for quantifying
vessel caliber.
Methods. Revised formulas were estimated using retinal
vessel measurements from 44 young adults free of hypertension and diabetes. Comparisons between the two methods
were done using digitized photographs from 4926 participants at the baseline examination of the Beaver Dam Eye
Study (BDES), an ongoing population-based cohort study
initiated in 1987. Individual arterioles and venules were measured using semi-automated computer software from which
summary measures were calculated.
Results. Correlation coefficients between the Parr-Hubbard and
revised formulas were high (Pearson correlation coefficients
ranging from 0.94 to 0.98). Both arteriolar and venular caliber
significantly increased with an increasing number of vessels
measured using the Parr-Hubbard formulas (p < 0.001), which
in turn affected the relationship to mean arterial blood pressure.
To the contrary, the revised formulas were not affected by the
number of measured vessels (p > 0.50).
Conclusions. We describe revised formulas for summarizing
retinal vessel diameters measured from fundus photographs
to be used in future studies and analyses. The revised
formulas correlate highly with the previously used ParrHubbard formulas, but offer the advantages of being
more robust against variability in the number of vessels
observed, being independent of image scale, and being easier
to implement.
Keywords: retinal vessels; arteriolar narrowing; hypertensive retinopathy; blood pressure; cardiovascular disease
Introduction
The retinal vascular system of the human eye is accessible to
direct and repeated observations in vivo. The characteristics
of its arterioles and venules in health and disease provide data
applicable to the study of systemic vascular disorders.1–15
In 1974 Parr et al.1,2 developed a method to quantify
retinal arteriolar caliber. In 1999 Hubbard et al.3 followed
Parr’s approach to quantify retinal venular caliber. Their
approaches took into account the relation between parent
trunk vessels and their two branches.
The Parr-Hubbard formulas have been used to summarize
retinal arteriolar and venular diameters measured from digitized photographs in various studies.11–15 While the computation of summary estimates of retinal vessel caliber from
these formulas was intuitively reasonable and the resulting
associations with blood pressure3,12 were in keeping with
expectations, we noted some features that could lead to
spurious variability in our estimates. For example, these
calculations allow contributions of a variable number of
vessel diameters for each eye to the overall estimate of
vessel caliber. This resulted in increasing trends between
the number of vessels included in the calculation and the
magnitude of summary estimates, potentially decreasing the
ability to discern real biological associations of vessel
caliber. In addition, the formulas include constant terms in
their equations, which in turn cause the result to be depen-
Received: April 21, 2003
Accepted: June 19, 2003
Correspondence: Michael D. Knudtson, Department of Ophthalmology, 610 N. Walnut Street, 4th floor WARF, Madison, WI 53726, USA.
Tel: +1-608-262-4202; Fax: +1-608-263-0279; E-mail: [email protected]
144
M.D. Knudtson et al.
dent upon the units (e.g., microns, pixels) of measurement.
We therefore developed revised formulas for summarizing
the caliber of arterioles and venules free of such constraints.
This paper compares these revised formulas with the previously used Parr-Hubbard formulas.
Materials and methods
Study populations
In this report we use data from two groups. Tenets of the
Declaration of Helsinki were followed. First, the revised
formulas were estimated from study photographs from 44
young adults free of hypertension and diabetes. This was the
same group Hubbard et al. used to develop the formula to
quantify venular caliber.3 Second, data from the Beaver
Dam Eye Study (BDES) was used for all other results presented. The BDES is a population-based cohort study of
age-related ocular diseases in adults, described in detail
elsewhere.16–18
Retinal vessel caliber measurements
Each group had their retinal vessels measured with different
technical procedures. In the 44 young normotensive subjects,
a 30° color retinal fundus photograph of the right eye centered on the disc (Diabetic Retinopathy Study Standard Field
119) was projected on white 19 ¥ 24 inch paper at a fixed distance. Edges of vessels that coursed through an area 0.5 to
1.0 disc diameters from the optic disc margin were marked
with a 0.5 mm lead pencil. Measurement at this distance from
the disc ensured that arteriolar status had been attained. All
photographs were projected at the same magnification.
Vessels widths were measured using a dial calipers, accurate
to 0.01 inches.
All Beaver Dam participants had stereoscopic 30° color
retinal photographs taken of both eyes, centered on the disc
(Diabetic Retinopathy Study Standard Field 1).19 Measurement of retinal vessel diameter has been described previously. In brief, these photographs were converted to digital
images by a high-resolution scanner (Fig. 1).15 Calibration of
the image was performed on the basis of the standard disc
diameter (1850 mm), as established by the Early Treatment
Diabetic Retinopathy Study, as a defined unit of measurement. The diameters of all arterioles and venules coursing
through a standard area 0.5 to 1.0 disc diameters from the
optic disc margin (Zone B in Fig. 1) were measured in
microns (3.8 mm per pixel) using a custom computer program
(Retinal Analysis, University of Wisconsin-Madison), according to a protocol described elsewhere.3,13
Parr-Hubbard formulas
The Parr-Hubbard method summarized the individual retinal
vessel measurements into the central retinal artery equivalent
Figure 1. Digitized retinal photograph. Zone A is a half-disc
diameter from the optic disc margin and Zone B is a half-disc to
one and half-disc diameter from the optic disc margin. Retinal
vessel diameter measurements are performed in Zone B.
(CRAE) and central retinal vein equivalent (CRVE).1–3 It has
been suggested that smaller arterioles (i.e. those farther away
from the optic nerve) are more affected by hypertension.20,21
For this reason the branches of arterioles were measured,
where possible, if the measurement of the trunk diameter
was ≥85 mm. Arteriolar caliber measurements were thus
combined into the CRAE as the branch variant (substituting
branch measurements for any trunk arteriole ≥85 mm) or the
trunk variant (using trunk measurements regardless of their
diameter). To correct for possible magnification errors, that
affect arterioles and venules similarly, the ratio between
CRAE (branch or trunk) to CRVE was calculated. For this
report we use CRAET (trunk variant), CRAEB (branch
variant), CRVE, AVRT (ratio using CRAET), and AVRB
(ratio using CRAEB) to abbreviate the Parr-Hubbard
summary measures.
Revised formulas
We have developed revised formulas to summarize the retinal
vessel diameters restricted to the six largest retinal arterioles
and venules measured from the photographs. To compensate
for the considerable variation in the number of bifurcations
in an eye, the relationship between trunks and branches
was expressed in terms of an empirically derived branching
coefficient:10
Branching Coefficient = (w12 + w 22 ) W 2
(1)
Revised formulas for summarizing retinal vessel diameters
where w1, w2, and W are, respectively, the widths of the narrower branch, the wider branch, and the parent trunk.
We estimated the branching coefficient for arterioles
and venules separately using data from the 44 young normotensive adults that Hubbard et al. used to develop
the venular formula.3 One hundred eighty-seven branchtrunk arteriole relationships were measured, yielding a
branching coefficient of 1.28, 95% CI = (1.25, 1.32), comparable to the cited theoretical branching coefficient of
1.26.22 One hundred fifty-one branch-trunk venule relationships were measured, yielding a branching coefficient of
1.11, 95% CI = (1.08, 1.14). We then inserted our estimates
of the branching coefficient into equation 1 and solved for W
to yield the following two formulas to approximate vessel
equivalents:
ˆ = 0.88 * (w12 + w 22 )1 2
Arterioles: W
(2)
ˆ = 0.95 * (w12 + w 22 )1 2
W
(3)
Venules:
where w1 and w2 are the same as described above, and Ŵis
the estimate of parent trunk arteriole or venule.
Using these formulas, including only the six largest arterioles and the six largest venules, we used an iterative procedure of pairing up the largest vessels with the smallest and
repeating until we reached a single number that we will still
call a central vessel equivalent. As an example, assume in a
retinal photograph the six largest arterioles are 100, 90, 80,
70, 60, and 50 mm. First put 100 and 50 into equation 4 to
yield 98.4 mm. Similarly pair up 90 and 60 to yield 95.2 mm
and 80 and 70 to yield 93.5 mm. After the first iteration there
are three values: 98.4, 95.2, and 93.5. Continue with the next
iteration by pairing up the largest and the smallest (98.4 and
93.5 to yield 119.4 mm). The middle number (95.2) carries
over to the final iteration. Finally, pairing up 119.4 and 95.2
yields 134.4 mm for CRAET-6.
Table 1.
145
The branches of arterioles ≥85 mm were still taken so
that we have a branch and trunk variant. For this report we
use CRAET-6, CRAEB-6, CRVE-6, AVRT-6, and AVRB-6 to
distinguish between the Parr-Hubbard and the revised
method. Definitions of other variables appear in other
reports.16,23,24
Statistical procedures
Age and summary indices of retinal vessel caliber were analyzed as continuous variables. Mean arterial blood pressure
(MABP) was analyzed both continuously and as a 6-level
ordered factor (<75, 75–84, 85–94, 95–104, 105–114, and
>114 mm Hg). The number of measured vessels (regardless
of the summary formula) was analyzed both continuously
and as a three-level ordered factor (arterioles: <9, 9–11, >11;
venules: <8, 8–10, >10). In most instances, ordinary linear
regression was used to evaluate significance. The correlation
between methods was assessed by the Pearson correlation
coefficient. Confidence intervals for correlations were calculated using methods presented by Snedecor and Cochran.25
We performed all analyses with SAS Version 8.0 (SAS
Institute Inc, Cary, NC).
Results
Table 1 shows the summary statistics for the two methods for
right eyes in the Beaver Dam population. The central retinal
vessel equivalents produced by the two methods correlate
quite highly, with Pearson correlation coefficients ranging
from 0.94 to 0.98. It should be noted that the mean ratio of
the arteriolar to the venular measure obtained from the
revised formulas is substantially smaller than that from the
Parr-Hubbard formulas. Coefficients of variation were
similar between the two methods.
Summary statistics for right eye vessel caliber.
Caliber
Method
N
Mean
SD
Coef. var
Corr.
Arteriolar
(Trunks)
Parr-Hubbard
Revised
4247
4226
195.0
165.3
18.4
15.4
9.4
9.3
0.96
Arteriolar
(Branches)
Parr-Hubbard
Revised
4247
4226
201.7
169.8
20.6
17.3
10.2
10.2
0.97
Venular
Parr-Hubbard
Revised
4248
4226
229.5
242.1
20.4
22.8
8.9
9.4
0.98
Ratio
(Trunks)
Parr-Hubbard
Revised
4247
4226
0.85
0.69
0.07
0.06
8.3
8.6
0.94
Ratio
(Branches)
Parr-Hubbard
Revised
4247
4226
0.88
0.70
0.08
0.07
9.0
9.3
0.95
N = Number of participants.
SD = Standard deviation.
Coef. var = Coefficient of variation (100 * (SD/Mean)).
Corr. = Pearson correlation coefficient.
146
M.D. Knudtson et al.
Figure 2 shows the relationship between the number of
measurable arterioles and venules and the central retinal
equivalents in right eyes, both from the entire Beaver
Dam population (n = 4157) and a subgroup of younger,
“normal” subjects (aged 43–50 years, free of hypertension,
cardiovascular disease, and diabetes (n = 690)). Using the
revised formulas, in the younger subgroup there was no association between the number of vessels and corresponding
central retinal equivalents (CRAET-6: p = 0.51; CRVE-6:
p = 0.79). In contrast, using the Parr-Hubbard formulas, in
the younger subgroup there was a strong increasing trend
between the number of vessels and corresponding central
retinal equivalents (for CRAET: p < 0.001; for CRVE: p <
0.001). In the whole population there was a significant
increasing trend with both methods, but the magnitude of
change was much more pronounced using the Parr-Hubbard
method.
Arteriolar caliber is known to decrease with an increase
in blood pressure. The Pearson correlation coefficient
between MABP and arteriolar caliber were similar for the
two methods (CRAET: -0.26, 95% CI = (-0.29, -0.22);
CRAET-6: -0.24, 95% CI = (-0.28, -0.20)). Venular caliber
was not significantly associated with MABP with either
method. We examined if stratifying by the number of measurable vessels has an effect on this relationship (Fig. 3).
After adjusting for age, for each category increase in the
number of arterioles CRAET increased by 3.3 mm, 95% CI
= (2.8, 3.7), whereas for each category increase in the
number of arterioles CRAET-6 did not significantly increase
(p > 0.05). Results were similar using the branch variants
instead of trunks (results not shown). Further, results were
similar for venules, with the Parr-Hubbard method more
affected by the number of venules than the revised method
(2.8 mm versus 1.0 mm increase for CRVE and CRVE-6,
respectively).
We further investigated the relationship between the
number of measured vessels and MABP. There was an
inverse relationship with MABP and the number of arterioles
(Pearson correlation = -0.09, 95% CI = (-0.13, -0.05)) and
there was no relationship between MABP and the number of
venules (Pearson correlation = -0.03, 95% CI = (-0.07,
0.01)).
Figure 2. Relationship between the summary measurements and the number of vessels measured (regardless of formula used) for the entire
Beaver Dam population and a younger sub-population. *young sub-population: ages 43–50, free of hypertension, diabetes, and cardiovascular disease.
Revised formulas for summarizing retinal vessel diameters
147
Figure 3. Relationship between the summary measurements and mean arterial blood pressure (MABP) stratified by categories of the number
of vessels measured. MABP is broken into 6 equidistant categories ranging 10 mm Hg (<75, 75–84, 85–94, 95–104, 105–114, and >114). The
horizontal axis is labeled at the midpoint of each of these categories.
Discussion
We have discovered several methodological issues with the
standard Parr-Hubbard formulas used in previous studies.11–15
First, the Parr-Hubbard formulas allow a variable number of
vessel diameters for each eye to affect the overall estimate of
vessel caliber. Second, the Parr-Hubbard formulas include
constant terms in their equations, making them sensitive to
scale. To address these issues, we developed revised formulas that summarize the retinal vessel diameters using the six
largest arterioles and venules measured from photographs.
The analyses presented comparing the methods showed that
the revised formulas were not affected by the number of
vessels measured and do not include constant terms in the
equation. We therefore believe that the revised formulas may
provide more precise and consistent estimates of retinal
vessel caliber in an eye than the previously used ParrHubbard formulas.
Compared to average vessel caliber using the ParrHubbard formulas, we note that venular caliber increased,
while arteriolar caliber decreased using the revised formulas
(Table 1). Although this was unexpected, we believe a mean
AVR of 0.69 calculated using the revised method was more
in keeping with biological expectations than a mean AVR of
0.85 calculated using the Parr-Hubbard method. Consistent
with this, Kagan et al. using a different measurement
approach reported mean arteriole to venule ratios of upper
temporal vessels ranging from 0.68 to 0.73.7
Parr et al. claimed that because the volume of a vascular
bed is related to the cross-sectional area of the feeding
vessels, the width of the central retinal artery should be
similar for normal eyes.1 Thus, the method for summarizing
retinal vessel diameters in normal eyes should theoretically
be independent of the number of vessels measured. By considering vessel caliber in a younger group free of known
disease to have “normal” eyes, we demonstrated that the
148
M.D. Knudtson et al.
number of vessels affected the summary values for the
Parr-Hubbard method, but not for the revised method
(Fig. 2). This provides further evidence that the revised
formula may be more robust compared to the Parr-Hubbard
formulas.
An inverse relationship between the number of vessels
to blood pressure has been reported by Kagan et al.7 We
found a similar inverse relationship with MABP in the
Beaver Dam population. Because results from the ParrHubbard formulas were clearly affected by the number of
measurable vessels (Fig. 2), the confounding effect of
using different numbers of vessels may decrease the ability
to discern biological associations by not considering the
number of measurable arterioles when assessing relationships between blood pressure and CRAET (Fig. 3). The
revised formulas did not have this problem because the relationship between blood pressure and CRAET-6 was independent of the number of arterioles measured. The results
were analogous for venules, although we did detect a slight
effect of the number of venules on the relationship between
blood pressure and CRVE-6.
The revised formulas (equations 2 and 3) do not
contain constant values as do the Parr-Hubbard formulas.
The latter were developed assuming that the vessels
would be measured in microns. Using different digital
photographic approaches, images may be measured in different units (e.g. pixels vs. microns), in which case the same
constant values would not apply. Our revised formulas can
be used on images of any magnification and measured with
any scale.
A technical advantage of using larger vessels is that they
are easier to measure.26 The color of the blood column is
more obvious, making it easier to type a vessel as an arteriole or venule, and the vessel walls are better defined, making
it easier to gauge the diameter accurately. We are currently
in the process of developing automated imaging software that
easily measures and identifies arteriole/venule status on the
larger vessels, but is less consistent for the smaller vessels.
Therefore using only large vessels in the summary formulas
greatly facilitates development of an automated retinal vessel
measurement system.
Earlier reports have used the Parr-Hubbard method, some
of which are included in the list of references.3,11–15 Reanalysis of some of those previously published analyses using the
revised formulas showed that overall associations did not
change and led to tighter confidence intervals (Knudtson et
al. unpublished data).
In conclusion we describe revised formulas for summarizing retinal vessel diameters measured from fundus
photographs to be used in future studies and analyses.
The revised formulas correlate highly with the previously
used Parr-Hubbard formulas and provide a comparable
representation of the vascular bed, but offer the advantages
of being robust to variability in the number of vessels
observed, being independent of image scale, and being easier
to implement.
Acknowledgements
This study was supported by the American Diabetes
Association Mentor Award (Klein R) and NIH grants
EYO6594 (Klein R, Klein BEK) and HL66018 (Klein R,
Wong TY).
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